On Ramsey properties of classes with forbidden trees

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On Ramsey properties of classes with forbidden treesLet $\F$ be a set of relational trees and let $\Forbh\F$ be the class of all structures that admit no homomorphism from any tree in $\F$; all this happens over a fixed finite relational signature $\sigma$. There is a natural way to expand $\Forbh\F$ by unary relations to an amalgamation class. This expanded class, enhanced with a linear ordering, has the Ramsey property.